$3\mathrm{.}2$ In a sequential batch machining operation, setup time is $1\mathrm{.}5$ hours and batch size is $120$ units. The cycle time consists of part handling time of $30sec$ and processing time of $2\mathrm{.}85$min. One part is produced each cycle. Tool changes must be performed every $10$ parts and this takes $2\mathrm{.}0$ min. Determine $($a$)$ average cycle time, $($b$)$ time to complete the batch, and $($c$)$ average production rate.